The general objective of the proposed research is to develop sequential statistical methods for the data monitoring of complex clinical trials in cancer. In many of these clinical trials, the principal outcomes include immediate responses that can be completely measured soon after a patient enters the study; or in many others, time to an event, responses recorded periodically over time, or events that recur over time. Sequential monitoring of responses of these types usually fit into a unified framework. In a large clinical trial when data are monitored, a test statistic computed sequentially over time forms a stochastic process which is approximately Gaussian. In many practical situations, this process has independent increments and can be rescaled to become the Brownian motion process. The applicant proposes to investigate the monitoring of the Brownian motion process from different points of view. Each of the proposed research topics is directly motivated by current and anticipated statistical needs for the design and data monitoring of clinical trials. The three specific topics of research proposed are : (1) two-sample sequential comparisons of changes in repeated measures; (2) sequential analysis of Poisson data under a random effects model; and (3) occasional or continuous data monitoring in clinical trials. Additional research topics will be identified as work proceeds on these projects and in response to discussions with Dr. David DeMets of the University of Wisconsin Clinical Cancer Center and Dr. Timothy Chen of the National Cancer Institutes.